An actual original, first issue machine would simply say "Macintosh" on the back.
As for what is inside, it could be any of three possibilities, and a distant 4th.
Original Macintosh
Macintosh 512
Macintosh 512e (800K drive).
The 512e's 800K drive is pretty easy to spot just looking in the front. But an 800K drive can also be used in place of a 400K drive and you'd get an 800K MFS volume if you don't have the ROMs. It needs to be the MFD-51W-03 kind only. Possibly the newer ones may work, but the oldest ones do not.
If you have the ROM upgrade, you have 800K HFS and 400K MFS support. No 800K MFS is possible with the ROM upgrade.
The distant 4th possibility?
A General Computer hard drive installed, some kind of MacSnap, Levco or other RAM upgrade hack job installed. I can usually tell by weight/handling if there is something more inside a Mac case, and I generally will not power up any of these machines without first opening them. If there's some kind of Levco board in there, there's an excellent chance that it's come loose and will make your day if you turn things on.